Download the PA 28 Service manual here:
www.mikeg.net/library/files/pa28-service.pdf .
The Piper Cherokee Generic inspection checklist begins on the first page of Table III-I.
There are notes at the end of the listing but this list does not include other must do inspection items such as airworthiness directive (AD) research and compliance for airframe, engine, propeller, and accessories such as magnetos, spark plugs, induction air filters, etc.
There is not FAA approved inspection checklist; each repair station or independent shop creates a check list or uses the checklist in the service manual as a general guideline.
Let me know if you have any other questions.